| Title:
|
A-Browder-type theorems for direct sums of operators (English) |
| Author:
|
Berkani, Mohammed |
| Author:
|
Sarih, Mustapha |
| Author:
|
Zariouh, Hassan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
99-108 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the stability of a-Browder-type theorems for orthogonal direct sums of operators. We give counterexamples which show that in general the properties $(\rm SBaw)$, $(\rm SBab)$, $(\rm SBw)$ and $(\rm SBb)$ are not preserved under direct sums of operators. \endgraf However, we prove that if $S$ and $T$ are bounded linear operators acting on Banach spaces and having the property $(\rm SBab)$, then $S\oplus T$ has the property $(\rm SBab)$ if and only if $\sigma _{\rm SBF_+^-}(S\oplus T)=\sigma _{\rm SBF_+^-}(S)\cup \sigma _{\rm SBF_+^-}(T)$, where $\sigma _{\rm SBF_{+}^{-}}(T)$ is the upper semi-B-Weyl spectrum of $T$. \endgraf We obtain analogous preservation results for the properties $(\rm SBaw)$, $(\rm SBb)$ and $(\rm SBw)$ with extra assumptions. (English) |
| Keyword:
|
property $(\rm SBaw)$ |
| Keyword:
|
property $(\rm SBab)$ |
| Keyword:
|
upper semi-B-Weyl spectrum |
| Keyword:
|
direct sum |
| MSC:
|
47A10 |
| MSC:
|
47A11 |
| MSC:
|
47A53 |
| MSC:
|
47A55 |
| idZBL:
|
Zbl 06562162 |
| idMR:
|
MR3475141 |
| DOI:
|
10.21136/MB.2016.8 |
| . |
| Date available:
|
2016-03-17T19:50:01Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144855 |
| . |
| Reference:
|
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